Chapter 4: Computational Tools for Inverse Problems

Learning Objectives

• Exploit Kronecker product structure in the sensing operator to reduce matrix-vector product cost from $O(M^2N^2)$ to $O(M_1N_1M_2 + M_2N_2N_1)$
• Implement matrix-free forward and adjoint operators using CuPy and PyTorch for GPU-accelerated imaging
• Distinguish forward-mode and reverse-mode automatic differentiation and choose the appropriate mode for imaging applications
• Design principled stopping criteria using primal/dual residuals, fixed-point residuals, and the discrepancy principle
• Warm-start iterative algorithms from the matched-filter image to accelerate convergence